Question: Simplify the expression. $ (7n^{5}-6n^{4}) - ( -n^{7}-6n^{5}-3n^{3}) $
Solution: Distribute any negative signs. $(7n^{5}-6n^{4}) + (n^{7}+6n^{5}+3n^{3})$ Since we are adding polynomials, we can simply remove the parentheses. $7n^{5}-6n^{4} + n^{7}+6n^{5}+3n^{3}$ Identify like terms. $ + \color{#DF0030}{7 n^5} - {6 n^4} + { n^7} + \color{#DF0030}{6 n^5} + \color{#9D38BD}{3 n^3} $ Combine like terms. $ { n^7} + \color{#DF0030}{ n^5} + { -6 n^4} + \color{#9D38BD}{ 3 n^3} $ Add the coefficients. $n^{7}+13n^{5}-6n^{4}+3n^{3}$